Question

The wavelength of the radiation emitted by a hot body depends on
A. Nature of its surface
B. Area of its surface
C. Temperature of its surface.
D. All of the above

Answer 1

Hint: To solve this question we should first of all find out the relation between wavelength of the radiation and surface of the hot body. Wien’s Law gives us the relation between the temperature of a black body and its wavelength at which the body emits light. Using this law, we will determine the factor on which radiation of a body depends.

Formula used:
\[\lambda =\dfrac{C}{T}\], Wien’s Law.

Complete step by step answer:
All the objects that are above the absolute zero temperature radiate energy. This energy is radiated as electromagnetic waves travelling at the speed of light. Various types of radiations are known today and each radiation has its defined wavelength. From the Wien’s law we can say that the wavelength of maximum emission for any body is inversely proportional to its absolute temperature.
\[\lambda =\dfrac{C}{T}\],
Where,
C = constant 2897
T = temperature of the body in Kelvin.
\[\lambda \] = wavelength of maximum emission.
According to this law, if the temperature of a body increases its wavelength of maximum emission decreases. So, from Wien’s Law it is clear that wavelength of the radiation depends on temperature of the surface.
Therefore, the correct answer is option C.

Additional Information:
We can solve this question just by knowing that every hot body emits radiation and simply thinking that radiation depends entirely on the temperature of the body. But thinking that the area of the surface would dissipate heat at lower temperature thus affecting wavelength of radiation is wrong. Students might get confused. So applying the formula is always better.

Note:
Students should study what a black body and black body radiation is. A black body is a physical body which absorbs all the incident electromagnetic radiation. The sun is an example of a black body as any incident radiation on the sun will be absorbed till it is lost completely.